Spontaneous symmetry breaking of population: Stochastic Lotka-Volterra model for competition among two similar preys and predators.

The celebrated Lotka-Volterra (LV) model is vastly used to describe the simple competition between prey and predator populations. The stochastic LV model, for its turn, considers the competition among two similar prey and two similar predator populations, with each group being described by identical mathematical equations. However, each of these groups differs in stochastic fluctuations, which are interpreted as small variations in each species' specimens (Genetic Diversity and Phenotypic Expression Diversity) and environmental conditions. The relative statistical variation presented is inversely proportional to the square root of the amount of specimens in each population. The model begins with two prey and two predator groups and, after a transient time, is reduced to one element of each group, returning to the classic LV system. That is, the model ends in asymmetric states despite starting from an initial symmetric condition without population excess. Spontaneous population symmetry breaking without population excess was obtained using the stochastic method. For its turn, the deterministic method could be used to analyze such breaking by forcing a perturbative fluctuation or adding little excess to one population, but the stochastic method can simulate such break in symmetry naturally.